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प्रश्न
Find the alternative arrangement using minimum switches for the following switching circuit.
बेरीज
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उत्तर
The symbolic form is
p ∧ [q ∨ {r ∧ (∼p ∨ (∼ q ∧ p)}]
= p ∧ [q ∨ {r ∧ ((∼p ∨∼ q) ∧ (∼ p ∨ p)] ....(Distributive law)
= p ∧ [q ∨ {r ∧ (∼p v ∼ q) ∧ T}] ....(Complement law)
= p ∧ [q ∨ {r ∧ (∼p ∨∼ q)}] ....(Identity law)
= p ∧ [(q ∨ r) ∧ (q ∨ (∼p ∨ ∼ q))] ....(Distributive law)
= p ∧ [(q ∨ r) ∧ {(q ∨∼ q) ∨ ∼ p}] ....(Assocative law)
= p ∧ [(q ∨ r) ∧ {T ∨ ∼ p}] ....(Complement law)
= p ∧ [(q ∨ r) ∧ T] ....(Identity law)
= p ∧ (q ∨ r) ....(Identity law)
∴ Alternative arrangement is
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